en
Scientific article
Open access
English

Viscous problems with a vanishing viscosity approximation in subregions: a new approach based on operator factorization

Published inESAIM. Proceedings, vol. 27, p. 272-288
Publication date2009
Abstract

In many applications the viscous terms become only important in parts of the computational domain. As a typical example serves the flow around the wing of an airplane, where close to the wing the viscous terms in the Navier Stokes equations are essential for the solution, while away from the wing, Euler's equations would suffice for the simulation. This leads to the interesting problem of finding coupling conditions between these two partial differential equations of different type. While coupling conditions have been developed in the literature, for example by using a limiting procedure on a globally viscous problem, we are interested here to develop coupling conditions which lead to coupled solutions which are as close as possible to the fully viscous solution. We develop our new approach on the one dimensional model problem of advection reaction diffusion equations with pure advection reaction approximation in subregions, which leads to the problem of coupling first and second order operators. Our guiding principle for finding transmission conditions is an operator factorization, and we show both analytically and numerically that the new coupling conditions lead to coupled solutions which are much closer to the fully viscous ones than other coupling conditions from the literature.

Citation (ISO format)
GANDER, Martin Jakob et al. Viscous problems with a vanishing viscosity approximation in subregions: a new approach based on operator factorization. In: ESAIM. Proceedings, 2009, vol. 27, p. 272–288. doi: 10.1051/proc/2009032
Main files (1)
Article (Accepted version)
accessLevelPublic
Identifiers
ISSN of the journal1270-900X
535views
487downloads

Technical informations

Creation03/16/2010 11:36:00 AM
First validation03/16/2010 11:36:00 AM
Update time03/14/2023 3:25:16 PM
Status update03/14/2023 3:25:15 PM
Last indexation01/15/2024 7:37:44 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack